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  1. J. T. Winthrop and C. R. Worthington, J. Opt. Soc. Am. 56, 588 (1966).
    [Crossref]
  2. C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
    [Crossref]
  3. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964), pp. 311–313 for list of requirements.
  4. Kirchhoff’s boundary conditions are sometimes used with Rayleigh’s integral formulas to solve diffraction problems. The resulting theory is called the Rayleigh-Sommerfeld diffraction theory. Wolf and Marchand give a thorough comparison between the Rayleigh-Sommerfeld and Fresnel-Kirchhoff theories: E. Wolf and E. W. Marchand, J. Opt. Soc. Am. 54, 587 (1964). E. W. Marchand and E. Wolf, J. Opt. Soc. Am. 56, 1712 (1966).
    [Crossref]
  5. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1965), 3rd ed., Sec. 11.7, Eq. 27.
  6. J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, New York, 1941), p. 363.
  7. H. G. Booker and P. C. Clemmow, Proc. Inst. Elec. Engrs (London) Pt. III,  97, 11 (1950).
  8. J. A. Ratcliffe, Rept. Progr. Phys. 19, 188 (1956).
    [Crossref]
  9. E. Wolf, Proc. Phys. Soc. (London) 74, 280 (1959).
  10. D. Gabor in Progress in Optics Vol. I, E. Wolf, editor (North-Holland Publishing Co., Amsterdam, 1961), p. 136.
  11. C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954), Eq. 2.18.
    [Crossref]
  12. H. Osterberg, J. Opt. Soc. Am. 55, 1467 (1965).
    [Crossref]
  13. A referee has indicated that John T. Winthrop has a derivation similar to that of this paper in his Ph.D. thesis, August1966, written at the University of Michigan, Ann Arbor, Mich.

1966 (1)

1965 (1)

1964 (1)

1959 (1)

E. Wolf, Proc. Phys. Soc. (London) 74, 280 (1959).

1956 (1)

J. A. Ratcliffe, Rept. Progr. Phys. 19, 188 (1956).
[Crossref]

1954 (2)

C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954), Eq. 2.18.
[Crossref]

C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
[Crossref]

1950 (1)

H. G. Booker and P. C. Clemmow, Proc. Inst. Elec. Engrs (London) Pt. III,  97, 11 (1950).

Booker, H. G.

H. G. Booker and P. C. Clemmow, Proc. Inst. Elec. Engrs (London) Pt. III,  97, 11 (1950).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1965), 3rd ed., Sec. 11.7, Eq. 27.

Bouwkamp, C. J.

C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954), Eq. 2.18.
[Crossref]

C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
[Crossref]

Clemmow, P. C.

H. G. Booker and P. C. Clemmow, Proc. Inst. Elec. Engrs (London) Pt. III,  97, 11 (1950).

Gabor, D.

D. Gabor in Progress in Optics Vol. I, E. Wolf, editor (North-Holland Publishing Co., Amsterdam, 1961), p. 136.

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964), pp. 311–313 for list of requirements.

Marchand, E. W.

Osterberg, H.

Ratcliffe, J. A.

J. A. Ratcliffe, Rept. Progr. Phys. 19, 188 (1956).
[Crossref]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, New York, 1941), p. 363.

Winthrop, J. T.

Winthrop, John T.

A referee has indicated that John T. Winthrop has a derivation similar to that of this paper in his Ph.D. thesis, August1966, written at the University of Michigan, Ann Arbor, Mich.

Wolf, E.

Worthington, C. R.

J. Opt. Soc. Am. (3)

Proc. Inst. Elec. Engrs (London) Pt. III (1)

H. G. Booker and P. C. Clemmow, Proc. Inst. Elec. Engrs (London) Pt. III,  97, 11 (1950).

Proc. Phys. Soc. (London) (1)

E. Wolf, Proc. Phys. Soc. (London) 74, 280 (1959).

Rept. Progr. Phys. (3)

J. A. Ratcliffe, Rept. Progr. Phys. 19, 188 (1956).
[Crossref]

C. J. Bouwkamp, Rept. Progr. Phys. 17, 39 (1954).
[Crossref]

C. J. Bouwkamp, Rept. Progr. Phys. 17, 35 (1954), Eq. 2.18.
[Crossref]

Other (5)

A referee has indicated that John T. Winthrop has a derivation similar to that of this paper in his Ph.D. thesis, August1966, written at the University of Michigan, Ann Arbor, Mich.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964), pp. 311–313 for list of requirements.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1965), 3rd ed., Sec. 11.7, Eq. 27.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, New York, 1941), p. 363.

D. Gabor in Progress in Optics Vol. I, E. Wolf, editor (North-Holland Publishing Co., Amsterdam, 1961), p. 136.

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Equations (18)

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2 f + k 2 f = 0
f ( x , y , z ) = - 1 2 π d x d y f ( x , y , 0 ) z ( e i k R R )             for             z 0 ,
f ( x , y , z ) = - 1 2 π - d x d y e i k R R [ z f ( x , y , z ) ] z = 0             for             z 0 ,
R = [ ( x - x ) 2 + ( y - y ) 2 + z 2 ] 1 2 .
- a ( x , y ) b ( x - x , y - y ) d x d y = - A ( p , q ) B ( p , q ) exp [ 2 π i ( p x + q y ) ] d p d q ,
H ( p , q ) = - h ( x , y ) exp [ - 2 π i ( p x + q y ) ] d x d y .
f ( x , y , z ) = - 1 2 π - d p d q F ( p , q ) G ( p , q ) exp [ 2 π i ( p x + q y ) ]             for             z 0 ,
f ( x , y , z ) = - 1 2 π - d p d q F ( p , q ) G ( p , q ) exp [ 2 π i ( p x + q y ) ] ,             for             z 0 ,
G ( p , q ) = - d x d y exp [ - 2 π i ( p x + q y ) ] { exp [ i k ( x 2 + y 2 + z 2 ) 1 2 ] ( x 2 + y 2 + z 2 ) 1 2 } ,
G ( p , q ) = - d x d y exp [ - 2 π i ( p x + q y ) ] z × { exp [ i k ( x 2 + y 2 + z 2 ) 1 2 ] ( x 2 + y 2 + z 2 ) 1 2 } .
exp [ i k ( x 2 + y 2 + z 2 ) 1 2 ] ( x 2 + y 2 + z 2 ) 1 2 = i 2 π - d p d q × exp { i [ p x + q y + ( k 2 - p 2 - q 2 ) 1 2 z ] } ( k 2 - p 2 - q 2 ) 1 2             for             z 0
G ( p , q ) = 2 π i exp { i [ k 2 - ( 2 π p ) 2 - ( 2 π q ) 2 ] 1 2 z } [ k 2 - ( 2 π p ) 2 - ( 2 π q ) 2 ] 1 2             for             z 0 ,
G ( p , q ) = - 2 π exp { i [ k 2 - ( 2 π p ) 2 - ( 2 π q ) 2 ] 1 2 z }             for             z 0.
f ( x , y , z ) = - d p d q F ( p , q ) exp [ 2 π i { p x + q y + 1 2 π × [ k 2 - ( 2 π p ) 2 - ( 2 π q ) 2 ] 1 2 z } ]             for             z 0 ,
f ( x , y , z ) = - i - d p d q F ( p , q ) [ k 2 - ( 2 π p ) 2 - ( 2 π q ) 2 ] 1 2 × exp [ 2 π i { p x + q y + 1 2 π [ k 2 - ( 2 π p ) 2 - ( 2 π q ) 2 ] 1 2 z } ] ,             for             z 0 ,
F ( p , q ) = - d x d y f ( x , y , 0 ) exp [ - 2 π i ( p x + q y ) ] ,
F ( p , q ) = - d x d y [ z f ( x , y , z ) ] z = 0 exp [ - 2 π i ( p x + q y ) ] .
F ( p , q ) = i [ k 2 - ( 2 π p ) 2 - ( 2 π q ) 2 ] 1 2 F ( p , q ) .